For the given quadrilateral to be a parallelogram, opposite sides must be congruent.
Therefore,
[tex]\begin{gathered} 24-x=x+6 \\ 24-6=x+x \\ 18=2x \\ x=9 \end{gathered}[/tex][tex]x+6=9+6=15[/tex]
Also, we have that:
[tex]\begin{gathered} y=2x+3 \\ \text{ Since }y=9\text{ it follows that:} \\ y=2(9)+3=18+3=21 \end{gathered}[/tex]
Therefore, y = 21 and x = 9
Hence, the perimeter is given by:
[tex]2(15+21)=72\text{ units}[/tex]
Therefore, the values of x and y are y = 21 and x = 9.
The perimeter is 72 units
